Critical Computation, Phase Transitions, and
Hierarchical Learning

James P. Crutchfield
Physics Department
University of California
Berkeley, California 94720, USA

Abstract

A study of the various routes to chaos in dynamical systems reveals that significant computation occurs at the onset of chaos. At first blush this is not surprising since statistical mechanics views these as phase transitions with infinite temporal correlations. In computational terms processes that are in a critical state, like those at the onset of chaos considered here, have an infinite memory. Storage capacity, however, is only part of information processing. The set of available nonlinear operations and just how the memory is organized are more important determinants of the class of computation that can be supported. This leads directly to studies of the architecture of information processing and to quantitative measures of complexity. There is a universal theory, for example, that indicates how complexity trades-off against the rate at which information is produced. This result suggests a new view of how learning and control systems can break out of inadequate internal models to discover genuinely new representations.

Citation

J. P. Crutchfield, Critical Computation, Phase Transitions, and, Hierarchical Learning in Towards the Harnessing of Chaos, Proceedings of the 7th Toyota Conference, M. Yamaguti, editor, Elsevier Science, Amsterdam (1994) in press.

Santa Fe Institute Working Paper 93-10-061.

Note

Based on a talk given at the Seventh Toyota Conference Towards the Harnessing of Chaos, Mikkabi, Japan, 1 November 1993.

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